1.1. Abstraction

Different types of objects and inheritances in Java.

Class

A class is a template to instantiate an object.

What is the relationship between a class and an object?

Let us create a class called Numeral that we want to be a super class of all numeral types:

package edu.emory.cs.algebraic;

public class Numeral {
}

• L1: packageindicates the name of the package that this class belongs to in a hierarchy.

• L3: public is an access-level modifier.

What are the acceptable access-level modifiers to declare a top-level class?

Let us declare a method, add() , that is an operation expected by all numeral types:

public class Numeral {
    /**
     * Adds `n` to this numeral.
     * @param n the numeral to be added.
     */
    public void add(Numeral n) { /* cannot be implemented */ }
}

• L4: @param adds a javadoc comment about the parameter.

The issue is that we cannot define the methods unless we know what specific numeral type this class should implement; in other words, it is too abstract to define those methods. Thus, we need to declare Numeral as a type of abstract class.

What are the advantages of havingNumeral as a super class of all numeral types?

There are two types of abstract classes in Java, abstract class and interface.

Can an object be instantiated by an abstract class or an interface?

Interface

Let us define Numeral as an interface:

public interface Numeral {
    void add(Numeral n);
}

• L2: abstract method

  • All methods in an interface are public that does not need to be explicitly coded.

  • Abstract methods in an interface are declared without their bodies.

Who defines the bodies of the abstract methods?

Let us create a new interface called SignedNumeral that inherits Numeral and adds two methods, flipSign() and subtract():

Can an interface inherit either an abstract class or a regular class?

public interface SignedNumeral extends Numeral {
    /** Flips the sign of this numeral. */
    void flipSign();

    /**
     * Subtracts `n` from this numeral.
     * @param n the numeral to be subtracted.
     */
    default void subtract(Numeral n) {
        n.flipSign();
        add(n);
        n.flipSign();
    }
}

• L1: extends inherits exactly one class or interface.

• L9: default allows an interface to define a method with its body (introduced in Java 8).

Can we call add() that is an abstract method without a body in the default method subtract()?

Although the logic of subtract() seems to be correct, n.flipSign() gives a compile error because n is a type of Numeral that does not include flipSign(), which is defined in SignedNumeral that is a subclass of Numeral.

What kind of a compile error does n.flipSign() cause?

There are three ways of handling this error: casting, polymorphism, and generics.

Casting

The first way is to downcast the type of n to SignedNumeral, which forces the compiler to think that n can invoke the flipSign() method:

default void subtract(Numeral n) {
    ((SignedNumeral)n).flipSign();
    add(n);
    ((SignedNumeral)n).flipSign();
}

This removes the compile error; however, it will likely cause a worse kind, a runtime error.

Why is a runtime error worse than a compile error?

Downcasting, although allowed in Java, is generally not recommended unless there is no other way of accomplishing the job without using it.

How can downcasting cause a runtime error in the above case?

Polymorphism

The second way is to change the type of n to SignedNumeral in the parameter setting:

default void subtract(SignedNumeral n) {
    n.flipSign();
    add(n);
    n.flipSign();
}

This seems to solve the issue. Then, what about add() defined in Numeral? Should we change its parameter type to SignedNumeral as well?

It is often the case that you do not have access to change the code in a super class unless you are the author of it. Even if you are the author, changing the code in a super class is not recommended.

Why is it not recommended to change the code in a super class?

How about we override the add() method as follows?

public interface SignedNumeral extends Numeral {
    @Override
    void add(SignedNumeral n);
    ...

• L2: @Override is a predefined annotation type to indicate the method is overridden.

The annotation @Override gives an error in this case because it is not considered an overriding.

What are the criteria to override a method?

When @Override is discarded, the error goes away and everything seems to be fine:

public interface SignedNumeral extends Numeral {
    void add(SignedNumeral n);
    ...

However, this is considered an overloading, which defines two separate methods for add(), one taking n as Numeral and the other taking it as SignedNumeral. Unfortunately, this would decrease the level of abstraction that we originally desired.

What are good use cases of method overriding and overloading?

Generics

The third way is to use generics, introduced in Java 5:

public interface Numeral<T extends Numeral<T>> {
    void add(T n);
}

• L1: T is a generic type that is a subtype of Numeral.

  • A generic type can be recursively defined as T extends Numeral<T>.

• L2: T is considered a viable type in this interface such that it can be used to declare add().

Can we define more than one generic type per interface or class?

The generic type T can be specified in a subclass of Numeral:

public interface SignedNumeral extends Numeral<SignedNumeral> {
    void flipSign();

    default void subtract(SignedNumeral n) {
        n.flipSign();
        add(n);
        n.flipSign();
    }
}

• L1: T is specified as SignedNumeral.

This would implicitly assign the parameter type of add() as follows:

void add(SignedNumeral n);

The issue is that the implementation of add() may require specific features defined in the subclass that is not available in SignedNumeral. Consider the following subclass inheriting SignedNumeral:

public class LongInteger implements SignedNumeral {
    @Override
    public void flipSign() { /* to be implemented */ }

    @Override
    public void add(SignedNumeral n) { /* to be implemented */ }
}

• L1: implements inherits multiple interfaces.
• L2-6: LongInteger is a regular class, so all abstract methods declared in the super classes must be defined in this class.

Since the n is typed to SignedNumeral in L6, it cannot call any method defined in LongInteger, which leads to the same issue addressed in the casting section.

Would the type of n being SignedNumeral an issue for the subtract() method as well?

Thus, SignedNumeral needs to define its own generic type and pass it onto Numeral:

public interface SignedNumeral<T extends SignedNumeral<T>> extends Numeral<T> {
    void flipSign();

    default void subtract(T n) {
        n.flipSign();
        add(n);
        n.flipSign();
    }
}

• L1: T is a generic type inheriting SignedNumeral, that implies all subclasses of SignedNumeral.

T can be safely passed onto Numeral because if it is a subclass of SignedNumeral, it must be a subclass of Numeral, which is how T is defined in the Numeral class.

Generics are used everywhere in Java, so it is important to understand the core concept of generics and be able to adapt it in your code to make it more modular.

Enum

Let us create an enum class called Sign to represent the "sign" of the numeral:

public enum Sign {
    POSITIVE,
    NEGATIVE;
}

• All items in an enum have the scope of static and the access-level of public.
• Items must be delimited by , and ends with ;.

The items in the enum can be assigned with specific values to make them more indicative (e.g., +, -):

public enum Sign {
    POSITIVE('+'),
    NEGATIVE('-');

    private final char value;

    Sign(char value) {
        this.value = value;
    }

    /** @return the value of the corresponding item. */
    public char value() {
        return value;
    }
}

• L5: final makes this field a constant, not a variable, such that the value cannot be updated later.
• L8: this points to the object created by this constructor.
• L11: @return adds a javadoc comment about the return value of this method.

Why should the member field value be private in the above example?

Note that value in L8 indicates the local parameter declared in the constructor whereas value in L13 indicates the member field declared in L5.

Limit of Interface

In SignedNumeral, it would be convenient to have a member field that indicates the sign of the numeral:

public interface SignedNumeral<T extends SignedNumeral<T>> extends Numeral<T> {
    Sign sign = Sign.POSITIVE;
    ...

• L2: All member fields of an interface are static and public.

Can you declare a member field in an interface without assigning a value?

Given the sign field, it may seem intuitive to define flipSign() as a default method:

/** Flips the sign of this numeral. */
default void flipSign() {
    sign = (sign == Sign.POSITIVE) ? Sign.NEGATIVE : Sign.POSITIVE;
}

• L3: condition ? A : B is a ternary expression that returns A if the condition is true; otherwise, it returns B.

Is there any advantage of using a ternary operator instead of using a regular if statement?

Unfortunately, this gives a compile error because sign is a constant whose value cannot be reassigned. An interface is not meant to define so many default methods, which were not even allowed before Java 8. For such explicit implementations, it is better to declare SignedNumeral as an abstract class instead.

Abstract Class

Let us turn SignedNumeral into an abstract class:

public abstract class SignedNumeral<T extends SignedNumeral<T>> implements Numeral<T> {
    /** The sign of this numeral. */
    protected Sign sign;

    /**
     * Create a signed numeral.
     * the default sign is {@link Sign#POSITIVE}.
     */
    public SignedNumeral() {
        this(Sign.POSITIVE);
    }

    /**
     * Create a signed numeral.
     * @param sign the sign of this numeral.
     */
    public SignedNumeral(Sign sign) {
        this.sign = sign;
    }
    ...

• L9: the default constructor with no parameter.

• L17: another constructor with the sign parameter.

• L10: this() calls the constructor in L17.

Why calling this(Sign.POSITIVE) in L10 instead of stating this.sign = Sign.POSITIVE?

    ...
    /** @return true if this numeral is positive; otherwise, false. */
    public boolean isPositive() {
        return sign == Sign.POSITIVE;
    }

    /** @return true if this numeral is negative; otherwise, false. */
    public boolean isNegative() {
        return sign == Sign.NEGATIVE;
    }

    /** Flips the sign of this numeral. */
    public void flipSign() {
        sign = isPositive() ? Sign.NEGATIVE : Sign.POSITIVE;
    }
    
    /**
     * Subtracts `n` from this numeral.
     * @param n the numeral to be subtracted.
     */
    public void subtract(T n) {
        n.flipSign(); add(n); n.flipSign();
    }

    /**
     * Multiplies `n` to this numeral.
     * @param n the numeral to be multiplied.
     */
    public abstract void multiply(T n);
}

• L29: abstract indicates that this is an abstract method.

Member fields and methods in an abstract class can be decorated by any modifiers, which need to be explicitly coded.

Is there anything that is not allowed in an abstract class but allowed in a regular class?

In summary, SignedNumeral includes 2 abstract methods, add() inherited from Numeral, and multiply() declared in this class.

Can you define an abstract class or an interface without declaring an abstract method?